%I #26 Feb 17 2021 03:54:25

%S 1,42,197,562,1257,2426,4237,6882,10577,15562,22101,30482,41017,54042,

%T 69917,89026,111777,138602,169957,206322,248201,296122,350637,412322,

%U 481777,559626,646517,743122,850137,968282,1098301,1240962,1397057

%N a(n) = N(5,n), where N(5,x) is the 5th Narayana polynomial.

%H G. C. Greubel, <a href="/A090198/b090198.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

%F a(n) = N(5, n) = Sum_{k>0} A001263(5, k)*n^(k-1) = n^4 +10*n^3 +20*n^2 +10*n +1.

%F G.f.: (1 +37*x -3*x^2 -13*x^3 +2*x^4)/(1-x)^5. - _Philippe Deléham_, Apr 03 2013

%F E.g.f.: (1 +41*x +57*x^2 +16*x^3 +x^4)*exp(x). - _G. C. Greubel_, Feb 16 2021

%p A090198:= n-> n^4 +10*n^3 +20*n^2 +10*n +1; seq(A090198(n), n=0..40) # _G. C. Greubel_, Feb 16 2021

%t LinearRecurrence[{5,-10,10,-5,1},{1,42,197,562,1257},40] (* _Harvey P. Dale_, Mar 06 2020 *)

%o (PARI) a(n) = n^4+10*n^3+20*n^2+10*n+1 \\ _Charles R Greathouse IV_, Jan 17 2012

%o (Sage) [n^4 +10*n^3 +20*n^2 +10*n +1 for n in (0..40)] # _G. C. Greubel_, Feb 16 2021

%o (Magma) [n^4 +10*n^3 +20*n^2 +10*n +1: n in [0..40]]; // _G. C. Greubel_, Feb 16 2021

%Y Cf. A001263, A008550, A090199, A090200.

%K nonn,easy

%O 0,2

%A _Philippe Deléham_, Jan 22 2004

%E Corrected by _T. D. Noe_, Nov 08 2006